There is a great deal of difference between qualitative and quantitative design, although there are some research methods that take a little bit from each category. Qualitative studies include ethnographies, case studies, and descriptive studies. This type of research aims to investigate and describe the process of the situation, be it an participant ethnography, or a world-wide internet survey. Qualitative researchers collect 6 sources of data: documentation, archival records, interviews/surveys, direct observation, participant observation, and physical artifacts. Quantitative research includes correlational research and experimental research, of which there are several types: true experiments, quasi-experiments, and many, many others. Quantitative research frequently uses randomly-selected sample groups and seeks to control as many variables as possible, especially in true experiments. It also poses a questions and a hypothesis as the basis of the research. Statistics come into play much more in quantitative research, including descriptive stats (mean, median, mode) and inferential stats (chi squared, t test, f test.) An important point from Morgan is that it is not useful to argue over the merits of one or the other, but that researchers should instead choose the method that best answers their particular question. Qualitative research designs are most useful in describing in-depth situations as they occur in “natural” settings -as things occur in “real-life.” Quantitative research designs are most useful in describing correlational and causal relationships between different phenomena or variables.
There is a clear difference between Validity and Reliability, although the two terms are often used incorrectly when talking about research. They are both forms of accuracy, but measure different things. Validity is the degree to which the researcher measures what (s)he claims to measure. Reliability is the external and internal consistency of the measurements. Both are needed for the research to have credibility (of the research methods), transferability (of the results to a new researcher), dependability (explaining results), and confirmability (repeatable results from a similar test). These four aspects can be analyzed to gauge the effectiveness of the research.
Statistical probability is a way of looking at research results. Total probabilities should always equal 1.0 and the results often form a bell-shaped distribution. Probability is a useful method to infer population distributions from the actual sample results. Significance is the degree of probability of the result occurring strictly from chance. In a well-controlled test, if a certain result is more than this- that is if it is statistically significant- then it can be inferred that the result is caused by the independent variable and not from random chance. Statistical significance is the difference between correlation and causation.